The article by James Franklin reminded me: Do you cover trope nominalism in Scholastic Metaphysics? In TLS and Aquinas (at least the half I've read so far), you only cover more basic, easily refutable forms of nominalism.

I hope both you and Ed will forgive me for answering on his behalf, but no, he doesn't. That's understandable; the problem of universals is not central to the book, especially in its modern form.

I actually think Ed mildly overstates the case for moderate realism as the mainstream Scholastic view. In my own view even Aquinas teetered on the fence between realism and nominalism (and I don't see that it was important to his arguments), and Scholastics like Abelard, Bonaventure, and Suárez defended views that have been called "moderate realism" but amount to what in modern terms we would call nominalism. Scotus (who has come up on this blog recently, and in the context of this book) stands out as one who unequivocally espoused the real existence of mind-independent universals.

I didn't find Keith's response very satisfying because I think his understanding of the metaphysical principles underlying Ed's arguments are quite confused. I'm curious what others here think.

I think Keith understanding of form is confused. I've never heard that substantial forms are as static and transmissible as Keith makes them out to be. He says:It appears that permanent, substantial, organic forms just cannot fit into this picture.

If my wife gave birth to the next evolution of the human race, like mutants in X-Men, then it doesn't follow that substantial forms have no explanatory value or are downright false altogether. To my mind, the only reason we know the difference between one generation and another is due to the substantial form. It doesn't make sense to throw the metaphysics of substantial form out with the baby's bathwater because the same substantial form didn't propagate between generations.

I also don't understand why he declares that forms are static. I am wake and I think rationally. I am asleep and I am not thinking rationally. Transubstantiation is a change that does occur, such as translation between life and death.

There's more I could say, such as failing to provide a compelling argument for moral obligation, but I actually would be interested to know what you guys (and maybe even Ed, if I could be so bold in suggesting it) think of what I've had to say above about Keith's understanding of the underlying metaphysics.

The Marilyn McCord Adams article was really good. It makes me think of Saint John of the Cross' passive purgation in his Ascent of Mount Carmel. One does not read that book without coming to understand that what is recounted there is something to be experienced, not simply something to be understood. It is more of a roadmap to a certain way of experiencing God where God is overwhelmingly participating in the exchange. We do not grasp God, he grasps us and the effect is called darkness because it so far surpasses what we can articulate in words.

I also like what she says about Scotus on the univocity of the concept of being. But isn't a certain amount of sameness implied in the equivocal concept of being as described by Aquinas? And isn't that samessness defined by the doctrine that the effect must be somehow contained in the cause? I know there must be much more to this discussion, but I am tempted to see this whole debate between Scotus and Aquinas as making a mountain out of a molehill and simply discount the entire issue.

Especially this part"No, the evident plasticity of organic natures derives from our best scientific knowledge about how evolution occurs, i.e. how genomes change and how alleles spread through successive populations. Molecular and population genetics are the drivers here, not metaphysics. Put simply, the basic reason why evolutionary biologists do not countenance irreducible teleology is just that, so far as they can tell, it just is not there! All organic functionality appears explicable in terms of random variation and selection by the (temporarily) ambient environment. Tendency to retain organic form is due to stabilizing selection, not, so far as anyone can tell, a metaphysical principle. Further, over geological time there is, as Darwin said, a tendency for populations to diverge from their ancestors to an indefinite degree. In one hundred fifty million years you can go from the dinosaur to the hummingbird.Of course, as you note, no empirical evidence can refute a metaphysical claim, though I think it can render it otiose. Intrinsic teleology might be there even though we cannot see it and have no need of it in our theories. Yet, Darwin was quite philosophically astute when he replied to Asa Gray—who suggested that variation might be divinely caused for ends that we cannot fathom—that to say that variation is planned but planned in a way that looks totally unplanned, is to utter a vacuity."

There's a related objections I heard from Bill Hasker. Moreland's a Thomistic dualist (TD) and Hasker was critiquing his stuff.He pointed out TD was associated with vitalism , which had failed and that it was incompatible with theistic evolution. If TD was true a certain transitional form (like Tiktaalik) was not really a transition , but a defective instance of the form of some other animal.Moreland is progressive creationist , so he said those criticisms didn't worry him.

What you have to understand is that substantial form is completely different from any form that can be perceived with the senses. All the latter are what we call accidental forms. All accidental forms, it's true, are subject to change and motion. The reason for this is that all accidental forms inhere in determinate matter, so if you alter the matter in which they inhere, you will thereby alter the form. For example, say you have some bronze that has the form of a sphere. If you alter the bronze in a certain way, you can change the sphere into a square. You can do this because the matter (bronze) is subject to alteration. Substantial form, on the other hand, does not inhere primarily in a matter that is subject to change; for it inheres in primary matter, which is just pure potency, and qua primary matter is not subject to any change or motion whatsoever. It is only subject to receiving one form or another. So unless a form already exists, there's no way that it can ever inhere in primary matter and be a substantial form. That's why any notion of new substantial forms coming into being is metaphysically absurd. All substantial forms are not only unchanging, they are also necessarily eternal.

To me at least, what you quoted from Parsons simply seems confused (which is ironic for someone who dismissed all theists as essentially intellectual dimwits not worth worrying about a few years ago).

He talks about genetics being a driver of the plasticity of organic natures, not metaphysics, as if you could somehow divorce what genetics could tell us about natures from metaphysics.

Otherwise, it is just question begging. Whether or not one can explain biological function in non-teleological terms is a vexed question (if not one where the evidence is against the naturalistic) that Dr. Feser has addressed many times. Maybe I'm wrong, but Parsons comes across as having a lot less knowledge of the subject of science and teleology than our host, so his attempts to lecture him are a little annoying.

Let's say there is a "formless" animal (a zombie kind of animal to borrow a term from phil. mind).The physical facts are all the same and materialism is true.Compare the zombie animal to the animal with the form. How are they different? I think that is what Parsons is saying when he says he thinks science made hylemorphism unnecessary.

But in A-T an animal by its very nature (so to speak) is a substance and has substantial form. I'm not the best person to reiterate the various arguments on the subject, but it is being a substance which gives one its identity, persistence over time, the capacity for accidents to inhere, and so on. And it is substantial form in matter that are the intrinsic causes of a material substance.

It makes no sense, therefore, to talk of an animal without form from an A-T perspective. The closest I can think of would be a dead animal, but this is not really, strictly speaking an animal (nor are its present substances without form).

One can argue against the A-T position, but it is a philosophical argument, which entails an interpretation of biological findings. It is not primarily something that can be settled by biological, or any other scientific, investigation.

Well, a Formless anything is an impossibility - the Formless animal in question would really be just a case of our mistaking another Substance or aggregate of Substances as an animal. Perhaps one could interpret it as claiming that living organisms are merely aggregates rather than Substances as some of the New Essentialists might hold, a claim which would certainly lead to odd consequences i.e. the Mind/Body relationship being dealt with in a Cartesian fashion or even after the manner of Leibniz monads. This has no bearing on irreducible teleology however since said feature is throughout the material world and not specific to living entities.

On an unrelated note: Not that here is the best place for it but I think the major failing of Natural Law Theory, or at least the version of it which is often put forward, is that it has arbitrarily been decided that Man’s orientation towards Transcendence is a ‘supernatural fact’ and thus is not factored into to what it means to be Rational (the focus is more on the Animal).

This may sound vile but I sometimes wonder if obscuring the Beyond is not part of the agenda, whether it be conscious or unconscious, of a percentage of modern Christians. Early Christian philosophers like Justin Martyr, Clement of Alexandria and Augustine looked on the eschatologies present in the Platonic philosophies with which they were familiar as an example of the sagacity of their original proponents. Thomas too held a similar view towards Pythagoras and Plato. Yet some moderns give the impression that they are glad Aristotle never gave much information on the after-life as it allows them to keep it behind the curtain of Revelation. (This is of course not to be taken as a criticism of Christianity as a whole any more than, say, a criticism of ID would be).

All Parsons is saying is that A-T concepts like form and final causes are not necessary to understanding biological phenomenon. He is suggesting, as naturalists tend to do, that naturalistic evolution can explain the development and functioning of living organs and organisms without these A-T concepts. But it does nothing to just appeal to genetics, as noted above. How one makes sense of the role of genetics in a philosophical sense depends upon whether one accepts A-T or some other framework.

I find Nagel's distinction between constitutive and historical accounts (though he applies the distinction to the mind). Pace George R.., it's my opinion that evolution is a strong historical account of how biological substances came about. (If someone rejects this, then it could straightforwardly be granted for the sake of argument, since it is not at issue in the debate between Feser and Parsons.) It also has implications for the way we look at the constitutive account of natural substances. But it is not a constitutive account and so doesn't eliminate an alternative constitutive account (ie. hylemorphism).

On the face of it, evolution could not ground teleology in any hard way. Upper-level features could often be realizable through a variety of evolutionary pathways, but if that is the case, then why should there be a different teleology associated with them, ie. why should a shark's doing what it makes it evolutionarily successful itself constitute what is good for a shark?

I'm adding nothing new here, but it may help to rephrase some of what's being said in another way.

Science alone doesn't rule in or out A-T metaphysics, or naturalist metaphysics, or just about any metaphysics. It at most provides data which we thereafter use and incorporate into our metaphysical views one way or the other. Saying 'Well we don't need A-T metaphysics because we have science' is a critical misfire, because metaphysics isn't in competition with science anyway. I think Parsons admits as much, but he's trying to get by by saying 'Well okay, science doesn't refute it, but we have this alternative understanding - so we don't need it!' Right, but the alternative understanding isn't 'science' but 'naturalism' - and plenty of critics argue that naturalism comes up wanting. 'But science!' will be of no help there.

By the way, I want to note something about this reply:

Yet, Darwin was quite philosophically astute when he replied to Asa Gray—who suggested that variation might be divinely caused for ends that we cannot fathom—that to say that variation is planned but planned in a way that looks totally unplanned, is to utter a vacuity."

That's nonsense. First, no, it's not a vacuity at all - because what matters is who variation 'looks totally unplanned' to. It's possible that variation looks totally unplanned to us, but does not look totally unplanned to God (or, for that matter, aliens or anyone else.) That's a key point being made. With regards to 'God' or 'design', the presence or lack of a plan is something science can't begin to test for.

Second, but related - variation doesn't even 'look totally unplanned' to everyone, much less does evolution as a whole. Since that question can't be settled by science*, the observation punts to subjective takes.

(* Anyone who claims it does can simply provide the research and experiment that tested for the plan of God, gods, etc in evolution. Peer reviewed, please. It either doesn't exist, or if it does, it will be an absolute joy to dismantle.)

William of Ockham was not wrong,wrong, wrong about the universality of individual concepts. In being like everything that they are like a concept represents all things of the same kind without any necessity for a Platonic identity of all those individual forms.

Jeremy writes:One can argue against the A-T position, but it is a philosophical argument, which entails an interpretation of biological findings. It is not primarily something that can be settled by biological, or any other scientific, investigation.

This is true.

For example, if the necessary existence of static substantial forms are demonstrated metaphysically, it makes no sense at all to say that empirical observations reveal otherwise, unless one wants to reject reason as the foundation for knowledge. It would be like saying that if I observed something coming into being without also perceiving what caused it to come into being, I would be justified in concluding that nothing caused it to come into being. The truth, of course, is that reason requires that the metaphysical principle that "everything that comes into being must have a cause" is what informs all observations, and all interpretations thereof.

Therefore, if evolution precludes the existence of static substantial forms, and such forms are demonstrably necessary, then it would be absurd and irrational to say that evolution has been observed. At most it can only seem to have been observed -- (and, in reality, it scarcely even rises to that level.)

CCT has already chuckled at the proper point in your post, so I'll let that pass. My overall point was simply that Doc Ock doesn't stop being a Scholastic just because someone disagrees with his nominalism.

I think what Parsons is saying makes sense.look at vitalism. Science hasn't falsified it , but we know so much about living things from science , it makes vitalism unnecessary. Vitalism doesn't explain anything.I think he is saying the same about science and Thomism.

My knowledge on this issue only goes so far, and not very far at that, but it seems like very bad thinking to say that since vitalism is moribund, so could Aristotelian teleology be. It's not enough to simply point out that some theories become outdated, and then suppose that another theory that rubs you the wrong way could just as well go the same way. It needs to be shown why the A-T view of causation, etc is like vitalism beyond the assertion that, like vitalism, it could be made superfluous.

In fact, it seems to me that there is an important way in which vitalism and A-T are not alike. The vitalist position, if I understand it correctly, supposes something immaterial that is a special sort of power of living things. If vitalism and A-T were both true, for the sake of argument, then vitalism would identify an aspect of the form of a living thing, not the form itself. The substantial form isn't, as I understand it, the sort of thing that can be healed or caused to work better or something like would be supposed of the 'vital forces'. Rather, the substantial form would be that principle whereby we judge just how healthy a thing is, what a good instance of that form it is, etc. On the face of it, it seems to be exactly the sort of principle one is invoking when one talks about the "fitness" of a particular organism, or "stabilizing selection" and so on.

Another way to put all this is to say that to suppose vitalism is true of living things is just to suppose something false about the form of living things in general, and contemporary biology is supposed to give us a more accurate account of that form. If one wanted to show that formal causes and the like were unnecessary, then one should show that one can talk about thing without appeals to teleology (e.g. "genomes change", "selection pressures", etc). Kant (if I understand him) understood that the problem was really the opposite of what Parson's makes it out to be. It is not that teleology might really exist, but is, at this point, unnecessary to invoke. Rather, the case is that we cannot speak of anything without some sort of teleological language, even if it were that teleology did not exist in reality.

In fact, it seems to me that there is an important way in which vitalism and A-T are not alike. The vitalist position, if I understand it correctly, supposes something immaterial that is a special sort of power of living things. If vitalism and A-T were both true, for the sake of argument, then vitalism would identify an aspect of the form of a living thing, not the form itself. The substantial form isn't, as I understand it, the sort of thing that can be healed or caused to work better or something like would be supposed of the 'vital forces'. Rather, the substantial form would be that principle whereby we judge just how healthy a thing is, what a good instance of that form it is, etc. On the face of it, it seems to be exactly the sort of principle one is invoking when one talks about the "fitness" of a particular organism, or "stabilizing selection" and so on.

I would say the difference is this: Vitalism is a hypothesis that there are vital forces (a sort of efficient cause) that make living things alive (or that make living things behave the way they do), whereas hylemorphism is a theory about the status of the facts disclosed by biology. Vitalism therefore is made superfluous by pointing out other efficient causes in a creature's physiology that sufficiently explain its life and behavior. There is not an analogous way to make hylemorphism superfluous, however, as its aim is not to provide efficient-causal explanations for particular phenomena.

look at vitalism. Science hasn't falsified it , but we know so much about living things from science , it makes vitalism unnecessary.

What were the claims of vitalism, and how has science made them unnecessary?

If the claim was, say... 'we'll never be able to generate an organic compound from inorganic matter', then scientific discoveries straightforwardly falsified a claim of vitalism - but that would mean vitalism is in that sense a defunct scientific theory, so the comparison doesn't work.

If the claim was something extraordinarily broad - 'living things differ fundamentally from non-living things in some ways' - then sure, science can't falsify it. But neither can science alone make the claim unnecessary. The statement has no claim built into it that determines what or how much knowledge we should draw from science. You can still come to a different conclusion, but science will largely be irrelevant to it.

I think he is saying the same about science and Thomism.

Sure, but how? So far his claim seems to be 'science provides such-and-such models about how living things operate - and these models don't directly mention metaphysical forces!' But neither the lack of mention is a surprise (science isn't philosophy/metaphysics, even if it's grounded in it) nor is the amount of knowledge (because Thomism doesn't preclude such scientific knowledge, and in fact implies the existence of the knowledge that science deals with.)

So, walk us through it. What is the Thomist claim, and how has science obviated it?

And as a fun aside - Paul Davies and John Gribbin declared that science killed materialism. The 20th century discoveries about quantum physics and matter obviated materialist claims. Do you agree with that?

I have enjoyed this, and Parsons has acquitted himself admirably. He really comes across as a reasonable person and not like one of these robotic new-atheists.

But his closing remarks strike me as little more than naturalist boilerplate.

Nothing he brings up from evolutionary biology even touches upon the questions of substantial form or intrinsic teleology.

David Oderberg and countless others have refuted the evolutionary argument against substantial form, and nobody on their side seems to have paid attention. If they had they would either up their game or stop trotting out these same bad arguments that have already been refuted over and over again.

He says that science renders teleology "otiose" and quotes Darwin.

This kind of thing is ubiquitous in contemporary analytic philosophy but none of it even rises to the level of an actual argument.

"Prominent scientist X said Y about Z" is not an argument for anything other than proposition Y, and in most cases it isn't even a particularly strong argument.

If intrinsic teleology is otiose then let's see the argument against it; "Darwin said so" is not an argument.

If this comment sounds intemperate it is because of my sheer frustration with the mindless scientism that currently dominates so much of analytic philosophy.

A property is one kind of "accident" (something that can't exist on its own but must inhere in something else). In particular, strictly speaking, a property (in Scholastic terms) is an accident that in some way follows from the essence of a substance.

A substance is just the opposite: it has a kind of independent existence (not independent of God or even of environmental circumstances, but it's self-contained in a way that properties are not).

A human being is a substance. Rationality is a property that follows from the essence of such a substance.

Partly as the next instalment in my one-man crusade for Phenomenology and partly due to the recent discussions of Hylemorphism I will make mention of Mark Kenneth Spencer’s Ph.D., Thomistic hylomorphism and the phenomenology of self-sensing, which I’m sure will be of interest to people here:

http://gradworks.umi.com/35/16/3516544.html

@Scott,

Cool, if you get a spare moment please let me know what you think of it. I’ve been meaning to look into his work on Evil at some point.

Talking of random Thomas volumes: has anyone any thoughts on W. J. Hankey’s God in Himself?

Despite their erroneous take on the Neo-Scholastics the NTs embarked on a noble labour in trying to set out a metaphysical anthropology of Divine-Human relationship (even if it was largely tainted by St. Heidegger). I admit I find it hard to comprehend why anyone should claim that desire of the Vision of God is not a natural desire, even if it be one doomed to perpetual frustration due to Original Sin. If God is, as Dante says, ‘the love that moves the Moon and Stars’ one would only expect human cultures to experience the pull of the Ground of Being, which is how the various religions arise.

It seems that after a certain date Christianity suffered a confusion of priorities. Certain notions common to both the Classical and The Medieval conscious were excluded from the natural order and reclassified as retrospective Revelation. When, with the advent of Protestantism and Kantianism, all knowledge of the Divine was withdrawn into the sphere of ‘faith’ and as the always tenuous popular understanding of theology waned God became nothing more than a character in a story book.

Sorry guys. I'm not as philosophically astute as you guys so I might have trouble conveying my ideas.

An analogy.Suppose there was a mousetrap on the table. Tommy A. says this trap has the form of a mousetrap and teleogical functions that allow it to trap rats. Now Keith looks at the mousetrap and dismantles it and re-assembles it. He performs a reductionistic analysis of the mousetrap. In his analysis he finds no reason to appeal to irreducible teleogical function or forms.

Now Keith hasn't necessarily refuted Tommy , but he has made Tommy's analysis unnecessary..That's what I think Parsons is saying. scientific reductionism has made Thomism unnecessary.

I agree, largely. The nature/supernature distinction is very much an early modern idea, and it represents two of that era's worst flaws: the tendency toward hyper-Augustinian fideism, and the tendency toward secular rationalism. In a way, Luther and Descartes are two sides of the same coin. The whole business would have been more-or-less incomprehensible to someone in the patristic or medieval period.

Now Keith hasn't necessarily refuted Tommy , but he has made Tommy's analysis unnecessary..

That presupposes that Tommy was attempting to give an efficient cause explanation with regards to the mousetrap.

This is an imperfect example, but consider this: Tommy says that the teleological purpose of a mousetrap is to catch rats. Keith disassembles the mousetrap, figures out how it works down to the atom. Has Tommy's analysis been made unnecessary?

Well, no. Because Tommy is talking about a teleological (and in this case extrinsic) purpose and direction for the mousetrap. Keith's analysis does nothing to refute Tommy's claim. In fact, it would seem no scientific study could refute Tommy, because Tommy's not making a scientific claim to begin with.

Now, in that second case Keith could insist 'But I took the mousetrap apart and I saw no 'purpose' there! Your explanation can be discarded, because we don't need that to explain the mechanical operation of a mousetrap!' It's just that Keith would be wrong, and likely confused.

"Suppose there was a mousetrap on the table. Tommy A. says this trap has the form of a mousetrap and teleogical functions that allow it to trap rats. Now Keith looks at the mousetrap and dismantles it and re-assembles it. He performs a reductionistic analysis of the mousetrap. In his analysis he finds no reason to appeal to irreducible teleo[lo]gical function or forms.

Now Keith hasn't necessarily refuted Tommy , but he has made Tommy's analysis unnecessary."

But he hasn't, unless he's found a way to explain the causal properties of the mousetrap without reference to the "aims" those causes accomplish.

Even a naturally occurring mousetrap (or something vaguely analogous—a Venus flytrap, say) has effects that it's by nature able to produce under the right conditions. And that just is teleology.

"That's what I think Parsons is saying. [S]cientific reductionism has made Thomism unnecessary."

What is necessarily missing from Keith's analysis, if it is genuinely reductionistic and based entirely on material decomposition and identification of assembly, is that the mousetrap is a mousetrap.

But even if we ignored this gaping inability on the part of Keith to recognize, if he is consistent, what the thing actually is, the parts of the mousetrap have stable causal capabilities essential to Keith's analysis in the first place. But stable causal capability is in Thomistic terms the most general form of ordinary final causality, or teleology if we want to call it that.

If Kieth Parsons is right, and science has done away with the rationale for substantial forms, then science must have come up with some OTHER reason for studying this mouse, and that tiger, and a meningitis bacterium...rather than this clump of stuff that includes the front half of a horse and part of a blanket and a little piece of saddle and 2 feet of dirt below. Or, that clump of matter that includes 13 people, a house, two airplanes, and the wave on top of the lake at the beach. Or some other clump of stuff that consists of 3 viruses and the Andromeda galaxy.

That is to say, they must have found some OTHER principle of integrity that makes the mouse, the tiger, and the bacterium each to be "a one thing" worthy of considering separately from other things, rather than stuff that is contiguous with other stuff and therefore of the same subject matter for study. But that's not what has happened - Lab doctors study rats, not rats-cages-floor-light-fixture aggregates. They know rats are different things than the cages. But they reject any principle by which to separate them out as separable because DISTINCT.

To be totally honest, I don’t see why Parson’s statement about living organisms should be allowed to be taken out of context since one would just argue the same metaphysics undergirds the molecular and particle levels just as much as the macro levels (in fact the New Essentialists feel more certain about it on that level). If he wants to argue for Mereological Nihilism he is welcome to but that’s really a whole other subject.

@ Scott,

Thanks, I shall read it along with David Alexander’s book on the same subject. I am not particularly interested in issues of Evil per se but the Fourth Way and the Transcendentals are something I want to study in more depth, and it ties in with it so they’ll likely turn up in my reading soon.

So something like 'height' is a property because independent of a substance (such as a man) that has that property there is no property of height.

This might sound stupid:but would a leg of a person be a substance or a property?I'm guessing it's a substance because you can refer to a leg independently of a body it was attached to.Which you can't do for height. You can't speak of height without some substance it's a property of.

@Kid CupiWhile Scott is busy these might help a little.“Proper 1 - distinctive; characteristic; special; pertaining to an attribute, accident, or object that necessarily belongs to a nature 2 - naturally adapted to some nature USES *proper* accident, concept, effect, knowledge, name object, sensible, term etc.”Note especially “proper accident.” It is a synonym of “property.”

“Property 1- *logic*, a proprium or proper difference; an attribute that does not form part of the essence of its subject, but necessarily results from that essence; a distinctive and characteristic attribute of a being.”

“Substance - a being whose essence naturally requires it to exist in itself; *ens per se; ens in se*; a being that has existence in itself and by virtue of itself as an ultimate distinct subject of being. Loosely it is equivalent to essence and nature.”

Scott, I find it quite surprising to hear that Aquinas sat on the fence between nominalism and (moderate) realism, given that he's in agreement with Aristotle on so much, and given just how much hinges on the question of universals.

I'm not saying you're wrong; you've clearly read far more than me; I'm just saying it's surprising, and that I've never heard it before.

Just offhand and subject to correction by others, I would say that having a leg may be a property, but the leg itself is neither a property nor a substance, just a part of a substance (and then only as long as the body to which it belongs is actually alive). It has its own form, certainly, but not a substantial form.

"[Y]ou can refer to a leg independently of a body it was attached to."

Loosely speaking, yes, you can, but strictly speaking, no, you can't. A severed leg is no longer a leg, properly speaking, but a lump of matter that used to be a leg.

@Edward (not Feser):

I'm not sure Aquinas ever directly addressed (or needed to address) the problem of universals. His account of form holds that (say) two dogs have forms that are numerically distinct but formally identical. Well, to my mind that's just a way of stating (one version or part of) the problem of universals, not a solution to it. It amounts to saying that each dog in some way "instantiates" the form of a dog, but sidestepping the question of whether one and the same form is literally present "in" each dog (or whether, in more Platonic language, they both "participate" in the same form). And that's fine; I don't think he needs a solution in order for his argument to work—and as I've posted before, I'm not sure forms were ever, for Plato at least, intended to be "universals" in the first place.

But (for example) accidents might be real universals. Suppose this book and that apple are the exact same shade of red; does that mean they literally have an accident in common, and that there is a single accident this precise shade of red "present in" both? I have yet to stumble across an answer from Aquinas—and I emphasize again that he may not need one.

At any rate his "moderate realism" comes down to the view that even though each dog has its own numerically distinct and individuated form, there's some sort of formal identity between the forms of any two dogs. So far as I can tell, this simply doesn't answer (and isn't intended to answer) the question of whether there is one single form literally common to both dogs. Scotus said quite unequivocally that there is; Aquinas, so far as I know, never did.

And Doc Ock thus wasn't just coming out of left field. If I'm right, the seeds of his view were sown by at least some of those who have been called "moderate realists"; as Paul Vincent Spade notes in his excellent introduction to Five Texts on the Medieval Problem of Universals, Boethius's "moderate realism" would today be called nominalism. I don't know whether the same observation would apply to Aquinas.

And yes, to be clear, you're right on the money about height. There can't be a real, actual, existing height without something that has it, just as there can't be red without something that is red or rationality apart from a being who is rational.

"So a leg apart from a body isn't a leg.Is that because the function of a leg is tied [to its] form? And with it being severed it can't perform it's function?"

Yep, more or less. A leg is by nature not a living organism in its own right but a part of a larger organism. Apart from that larger organism, it can't serve as a leg and it can't survive independently.

Interesting. Someday hopefully I will get to read it. I have been a bit on the fence about the Aristotelian position on mathematics (though my thoughts on the matter aren't really clear either). William Wallace, in The Modeling of Nature, says that numbers like 5 are "real" in that they are instances of the abstracted accident of quantity, but 0 is an entia rationis. I agree with the latter point but am inclined to think that the same reasoning applies to the former. General ideas about continuous and discrete quantities, I think, I would be willing to admit as real entities, but anything very formal, I would consider a being of reason.

@GregProfessor Franklin stakes out a middle ground between Platonism and nominalism. He calls his version “semi-Platonist” or “modal” Aristotelianism. I’m only on chapter 2. But I’m looking forward to the discussion of infinity, under the rubric of “uninstantiated universals.” Please don’t get the impression that I’m a math whiz. Hardly. And I’m a novice to Thomism. But I’ve had a lifelong interest in the foundations of mathematics. I’ve never been able to think of it as just a tool. I want it to say something about reality, hence my interest in the book. I should add that I ordered the book via Amazon.

One might say that normal numbers are ens rationis fundamento in rei, that is beings of reason with an objective foundation in reality like Universals, whilst Zero is an ens rationis pure and simple (any five objects can serve as the basis for the emptied out Formal Identities which constitute the number 5 whilst Zero is founded on nothing save for a need in our thought processes). There can be Relations or Categorical Forms from which we may derive the number 5 but there are none from which we can derive via formalisation the 'number' Zero

There are real instances of the universal "being 5 in number" in the world but no such instances of 0. Therefore 0 is an “entia rationis” a mental thing?

That seems to be Wallace's position. There does not exist anything such that there "are" 0 of that thing. But we have the concept of 0 because, knowing what things are, we can consider what it would be like if there were not some thing (ie. a thing minus itself).

So, are you saying that five is in some sense also an “entia rationis”? Or is zero, like five, somehow instantiated? Or have I misread you altogether?

I was saying that 5 is an entia rationis as well as 0. However I do think there is a sense in which 5 is instantiated while 0 is not, so I do not regard the cases as exactly analogous. I just do not feel confident that, for instance, if I see a grove of 5 trees, there is a universal "5" present. Again, my reasoning here is not very clear--but the number designating how many trees there are seems to me to be more "perspectival" and mind-dependent than are other forms (ie. the forms of the trees themselves). I do think that Daniel's "ens rationis fundamento in rei" gets at the right idea. That was not a distinction that Wallace employed.

I jumped ahead to Professor Franklin’s brief section on zero. His position seems to be very close to Wallace’s as you’ve stated it. I haven’t gotten to his views on natural numbers specifically. Your main question seems to concern the degree to which universals are mind-independent. I think Professor Franklin would say they are mainly mind-independent. In the introduction (page 5-6) he asks us to imagine, as far as we can, the world before there were humans around, a purely physical world; “Is there or is there not, in that world, anything of a mathematical nature (to speak as noncommittally as possible)?” In short his answer is “Yes.” […] Similarly with discrete quantity. Parts of the world, prior to any naming operation, come in discrete chunks that are identical in some respect; for example electrons identical in mass and charge, and apples having close similarities in shape, size and biochemistry.”

I’ll try to keep you abreast of things that seem to address your concerns as I go.

For example, again with the grove of 5 trees, the universal 5 would be present. So would the universals 4, 3, 2, and 1.

Another question would be about fractions, like 2.5. That seems like a being of reason to me. The rational numbers are an extension of the natural numbers. But it can be used to represent some concrete idea about continuous quantity. (Or even discrete, if I am talking about two things and half of another.) But is if I have two and a half apples, surely there isn't a universal two-point-fiveness. (This is a separate question of course. I could see rational numbers as beings of reason even if natural numbers are something stronger.)

I’ll try to keep you abreast of things that seem to address your concerns as I go.

I have read James Franklin's book and I have to say I have some problems with it; as he seems to have a poor grasp of the nature of mathematical, second order, abstraction.

After having long delayed it, I have started struggling with Mullahy's Phd Thesis "Thomism and Mathematical Physics" finished under the direction of De Koninck and for now, I will just say: the nature of mathematical abstraction is treated in chapter VI; many important points were made in chapter II but they are briefly reviewed at the beginning of the chapter.

Is “tree” more surely a universal than 5 or 2.5? You seem to have a scale in mind along which things can be more or less universal. On that scale it seems to me “tree” would be a solid universal, 5 somewhat less universal, 2.5 or 0 would be not universal at all. Would this scale be related to or would it represent degrees of mind-dependence, the tree being the least mind-dependent, 0 being the most?

Is “tree” more surely a universal than 5 or 2.5? You seem to have a scale in mind along which things can be more or less universal. On that scale it seems to me “tree” would be a solid universal, 5 somewhat less universal, 2.5 or 0 would be not universal at all. Would this scale be related to or would it represent degrees of mind-dependence, the tree being the least mind-dependent, 0 being the most?

I think something is a universal or it isn't. When I express my doubts about 5 and 2.5, I don't really think of them as "less" universal but as possibly (epistemically) not universals. (Mind dependence is associated with this ordering. But I think genuine universals will all be mind-independent.)

I’m up to chapter 6. I’m not sure the professor is going to address universals at length. He says things like “Thus, for example, the universal ‘being 1.57 kilograms in mass’ stands in a certain relation, a ratio, to the universal ‘being 0.35 kilograms in mass’.” (page 35) He doesn’t say what criteria make these mixed numbers universals, or valid components of universals.

Chapter 5 reminded me of a lengthy debate I once had at the “Critical Cafe” (a Popperian site). One or two scientists were arguing for “Necessary truths about reality” with different examples from those used by Professor Franklin. I was arguing the other side. But I had to concede that they were on to something.

Something tells me that I won’t come across the material most of interest to you until pretty far along. But I’ll try to keep you updated nevertheless.

With Aristotle, I thought that the concept of the potentially infinite was unproblematic. Professor Franlkin quotes an unnamed (because unknown) Schoolman who argued against it, reductio ad absurdum, as follows.

“Suppose the concept of potential infinity is coherent. Then it is possible that the world has existed for a potential infinity of past days. Suppose that on each of those days, an angel laid down a grain of sand. How many grains of sand are there now? There must be an actual infinity. Therefore, potential infinity implies actual infinity.” Page 139

I can’t seem to imagine or conceive of a *potential* infinity of past days. I’m just not clear on what that would mean. A potential day past would be a day that could have happened, but didn’t. But if there were such a day anywhere in the series, wouldn’t the rest of the series be cut off? What if instead I consider the series as a whole? A potential series of past days is a series that could have unfolded, but didn’t. But now I find that if I put a grain of sand in a bucket for each of those potential days, I have an infinite number of grains. Okay, now I think I follow the Schoolman’s argument.

I’m left with the question of how one assume’s the absurd at the beginning of an argument. What if I said “Assume (then I let my cat walk over the keyboard). What is it one is assuming?

Philoponus, a Christian Neo-Platonic, argued against any human concept of "infinity" or "eternity" by stating as a fact of human experience that a human being cannot literally conceive or experience infinity or eternity. Therefore limits to the past are built-into rational thought, thereby making Creation at a specific point in time more rational because it is coherent in finite human thought and finite experience as opposed to the eternal existence of the universe. This has problems that are, however, NOT insurmountable. "Infinity" and "eternity" become unknowns in any equation. Galileo read Philoponus and took advantage of this way of thinking to always presuppose starting & ending points to movement even though he knew, also from experience, there was always a "before" and "after". This may be one of the reasons the "big bang theory" is starting to have difficulties that still can be overcome by simply following a similar line of thought. But I am out of my depth here.

Thanks to those who commented on my book An Aristotelian Realist Philosophy of Mathematics. It's Aristotelian realist in spirit, but it doesn't accept the Thomist theory that mathematics differs from natural sciences via "intelligible matter" or a different "level of abstraction".

About Me

I am a writer and philosopher living in Los Angeles. I teach philosophy at Pasadena City College. My primary academic research interests are in the philosophy of mind, moral and political philosophy, and philosophy of religion. I also write on politics, from a conservative point of view; and on religion, from a traditional Roman Catholic perspective.